An atomic force Microscope (hereinafter, referred to as an AFM) is a device that uses, as a force sensor, a cantilever with a sharp tip (probe) at its end to generate fine image of uneven sample surface (for example, see Patent Literature 1).
More specifically, when the probe of the cantilever is brought into proximity of a sample, interaction force is exerted between the probe and the sample. The interaction force is detected, and the position of the probe in perpendicular to the sample is controlled to keep the interaction force constant. In this state, when the probe is scanned in parallel to the sample, the probe is oscillated across the uneven surface of the sample. The AFM records the contours of the surface at positions in the parallel direction to generate an image of the uneven sample surface.
Depending on the method of detecting the probe-to-sample interaction force by using the cantilever, the AFM can be operated in two kinds of operation modes: (A) static mode and (B) dynamic mode.
The AFM in the static mode detects probe-to-sample interaction force according to a displacement of the cantilever caused by the probe-to-sample interaction force.
The AFM in the dynamic mode, on the other hand, detects probe-to-sample interaction force according to oscillation amplitude, frequency, or change in phase which result from the probe-to-sample interaction force when the cantilever is mechanically oscillated at a frequency at or close to its resonance frequency to be scanned in parallel to the sample.
There is a known method of measuring potential distribution on an uneven sample surface as well as image of the uneven sample surface by using these AFMs (for example, see Non Patent Literature 1).
FIG. 6 is a schematic diagram showing the principle of Kelvin Probe Force Microscopy (hereinafter, referred to as “KPFM”) which is widely known as a potential measurement device using the AFM.
As shown in FIG. 6, a KPFM 800 includes a cantilever 204, a probe 223, a sample 205, an AC source 201, and a DC source 952.
The cantilever 204 has a sharp tip (probe) 223 at its end. The cantilever has one free end with the probe and the other fixed end.
The sample 205 is an object to be measured which is set in air or vacuum.
The AC source 201 is a power-supply device that applies an AC bias voltage denoted as Vac COS(ωmt) between the probe 223 and the sample 205. Here, Vac denotes an amplitude of the AC voltage, and ωm denotes a frequency of the AC voltage.
The DC source 952 is a power-supply device that applies a DC bias voltage denoted as Vdc between the probe 223 and the sample 205.
On the surface of the sample 205, potential distribution Vs exists due to distribution of electric charges, polarization, work function, and the like. Therefore, a probe-to-sample potential difference Vts after applying bias voltages by the AC source 201 and the DC source 952 is determined by following Equation 1.[Math. 1]Vts=Vdc−Vs+Vac cos(ωmt)  (Equation 1)
In Equation 1, the direction from the top surface to the rear surface of the sample 205 is considered as a positive direction, assuming that the top surface is a surface facing the probe 223 and the rear surface is the other surface among the both surfaces of the sample 205. A coordinate axis of this direction is hereinafter referred to as a z axis. If a probe-to-sample electrostatic capacitance is Cts, probe-to-sample electrostatic force Fes is determined by following Equation 2.
                    [                  Math          .                                          ⁢          2                ]                                                                                                                F                es                            =                            ⁢                                                1                  2                                ⁢                                                      ∂                                          C                      ts                                                                            ∂                    z                                                  ⁢                                  V                  ts                  2                                                                                                        =                            ⁢                                                1                  2                                ⁢                                                                            ∂                                              C                        ts                                                                                    ∂                      z                                                        [                                                                                    (                                                                              V                            dc                                                    -                                                      V                            s                                                                          )                                            2                                        +                                                                                                                                        ⁢                                                                    1                    2                                    ⁢                                      V                    ac                    2                                                  +                                  2                  ⁢                                      (                                                                  V                        dc                                            -                                              V                        s                                                              )                                    ⁢                                      V                    ac                                    ⁢                                      cos                    ⁡                                          (                                                                        ω                          m                                                ⁢                        t                                            )                                                                      +                                  1                  2                                                                                        (                  Equation          ⁢                                          ⁢          2                )            
As seen in Equation 2, Fes includes (1) DC components (the first and second members on the right-hand side of Equation 2), (2) ωm component (the third member on the right-hand side of Equation 2) among AC components, (3) 2ωm component (the fourth member on the right-hand side of Equation 2) among AC components.
Here, Fes can be measured as displacement, oscillation amplitude, frequency, or change in phase of the cantilever. The KPFM 800 detects only the ωm component (namely, the third member on the right-hand side of Equation 2) included in the measured Fes, by using a lock-in amplifier (not shown).
As seen in Equation 2, as the ωm component is proportional to (Vdc−Vs), feedback control is performed on Vdc to cancel (set to zero) the ωm component to always establish Vdc=Vs. In this condition, the probe 223 is scanned in parallel to the sample 205 and values of Vdc are recorded at positions of the probe in parallel to the sample to generate image of potential distribution of the surface of the sample 205.
Another known potential measurement device using AFM is Scanning Maxwell Stress Microscopy (hereinafter, referred to as SMM).
Although the SMM measures an electrical potential (hereinafter, referred to as a “potential”) of a surface based on the same principle as that of the KPFM, the SMM differs from the KPFM in the method of controlling a probe-to-sample distance. In the same manner as the typical AFM in dynamic mode, the KPFM controls positions of the probe 223 in perpendicular to a sample to keep constant oscillation amplitude, frequency, or change in phase of the cantilever. The SMM, however, controls positions of the probe in perpendicular to a sample to keep constant 2ωm component (the fourth member on the right-hand side of Equation 2) occurred by an AC bias voltage.